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arXiv 1901.07372physics.opticsnlin.CDquant-ph
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超越耦合伊辛自旋的耦合参量振子理论

Theory of coupled parametric oscillators beyond coupled Ising spins

Marcello Calvanese Strinati, Leon Bello, Avi Pe'er, Emanuele G. Dalla Torre

摘要:

周期性驱动的参量振荡器提供了一种方便的方法来模拟经典的伊辛自旋。当许多参数振荡器耗散耦合时,它们可以类似于伊辛自旋网络,形成有效的相干伊辛机(CIM),有效地解决计算困难的优化问题。在相应的论文中,我们实验研究了CIM的最小实现,即两个耦合参量振荡器[L.贝洛湾Calvanese Strinati,E. G. Dalla Torre和A. Peer,Phys. Rev. Lett. 123,083901(2019)]。我们发现,振荡器之间的能量守恒耦合可以极大地改变动力学,导致永恒的节拍,这超越了伊辛描述。在这里,我们分析了这种效应理论上解决数值,并在可能的情况下,分析两个参数振荡器的运动方程。我们的主要工具包括:(i)Floquet分析的线性方程组,(ii)多尺度分析的基础上分离的时间尺度之间的参数振荡和拍,和(iii)极限环和吸引子的数值识别。使用这些工具,我们完全确定的相位边界和临界指数的模型,作为一个函数的强度和相位的耦合和泵。我们的研究突出了相图的普遍性和它对系统中存在的特定类型的非线性的独立性。此外,我们确定了新的阶段的模型与两个以上的吸引子,可能描述一个更大的自旋代数。

英文摘要:

Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent Ising machine (CIM) that efficiently solves computationally hard optimization problems. In the companion paper, we studied experimentally the minimal realization of a CIM, i.e. two coupled parametric oscillators [L. Bello, M. Calvanese Strinati, E. G. Dalla Torre, and A. Pe'er, Phys. Rev. Lett. 123, 083901 (2019)]. We found that the presence of an energy-conserving coupling between the oscillators can dramatically change the dynamics, leading to everlasting beats, which transcend the Ising description. Here, we analyze this effect theoretically by solving numerically and, when possible, analytically the equations of motion of two parametric oscillators. Our main tools include: (i) a Floquet analysis of the linear equations, (ii) a multi-scale analysis based on a separation of time scales between the parametric oscillations and the beats, and (iii) the numerical identification of limit cycles and attractors. Using these tools, we fully determine the phase boundaries and critical exponents of the model, as a function of the intensity and the phase of the coupling and of the pump. Our study highlights the universal character of the phase diagram and its independence on the specific type of nonlinearity present in the system. Furthermore, we identify new phases of the model with more than two attractors, possibly describing a larger spin algebra.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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